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arXiv · 1404.5238

KSGNS type construction for $\alpha $-completely positive maps on Krein $C^{\ast}$-modules

Mohammad Sal Moslehian·Maria Joita·Un Cig Ji
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Abstract

In this paper, we investigate $\Phi$-maps associated to a certain type of $\alpha$-completely positive maps. We then prove a KSGNS (Kasparov--Stinespring--Gel'fand--Naimark--Segal) type theorem for $\alpha $-completely positive maps on Krein $C^*$-modules and show that the minimal KSGNS construction is unique up to unitary equivalence. We also establish a covariant version of the KSGNS type theorem for a covariant $\alpha $-completely positive map and study the structure of minimal covariant KSGNS constructions.

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BibTeXRIS

Mohammad Sal Moslehian, Maria Joita, Un Cig Ji. 2014-04-21. KSGNS type construction for $\alpha $-completely positive maps on Krein $C^{\ast}$-modules. https://doi.org/10.1007/s11785-015-0520-5

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